If cos2θ - sin2θ - 3cosθ + 2 = 0, 0° < θ < 90°, then what is the value of 4 cosecθ + cotθ?
Show answer & explanation
Correct answer: A
Explanation
Correct Answer is option 1 i.e. 3√3
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Concept |
Understanding |
Application |
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Cos60 = ½ sin2θ = 1 – cos2θ |
Given cos2θ - sin2θ - 3cosθ + 2 = 0 |
cos2θ - sin2θ - 3cosθ + 2 = 0 ⇒ cos2θ - 1 + cos2θ - 3cosθ + 2 = 0 ⇒ 2cos2θ - 3cosθ + 1 = 0 ⇒ 2cos2θ - 2cosθ - cosθ + 2 = 0 ⇒ 2cosθ(cosθ – 1) – 1(cosθ – 1) ⇒ (2cosθ – 1) (cosθ – 1) = 0 ⇒ cosθ = 1, ½ But given that 0 < θ < 90 Since cos 0 = 1 but θ can’t be 0. Hence, Cosθ = ½ θ = 60 Now, 4cosecθ + cotθ = 4 × 2/√3 + 1/√3 = 9/√3 = 3√3 |